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%I #21 Dec 29 2016 03:55:23
%S -5,-6,-9,-18,-26,-34,-123,-107,3953,90021,203866,678250,3860926,
%T 62168609,1022130830,22777519100,46323907000,1499885420000,
%U 47625567000000,318447820000000,974228630000000,36070436000000000
%N a(n) = floor( exp(gamma) k log log k ) - sigma(k), where gamma is Euler's constant (A001620) and sigma(k) is sum of divisors of k (A000203), the n-th colossally abundant number (A004490).
%C By Robin's theorem, if the Riemann hypothesis is true the only negative values this sequence attains are the first eight terms; if it is false, it becomes negative again somewhere farther on. Briggs conjectured, in effect, that this sequence is asymptotic to C k / sqrt(log(k)) for some constant C.
%D G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
%H Keith Briggs, <a href="https://projecteuclid.org/euclid.em/1175789744">Abundant numbers and the Riemann Hypothesis</a>, Experimental Math., Vol. 16 (2006), p. 251-256.
%Y Cf. A004490, A058209.
%K sign
%O 2,1
%A _Gene Ward Smith_, Dec 17 2016